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Updated: Aug 5, 2025

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
Published on: January 31, 2020
Nonlinear Diffusion for Bacterial Traveling Wave Phenomenon
Yong-Jung Kim1, Masayasu Mimura2, Changwook Yoon3
1Department of Mathematical Sciences, KAIST, Daejeon, 34141, Republic of Korea.
Abstract:
The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher-KPP equation. For this reason, the Keller-Segel equations are widely used for bacterial waves. Note that the Keller-Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.
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